单复变函数第2版（英文版）
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作者（美）J B 康威（J B Conway) 著
出版社世界图书出版公司
ISBN9787506271912
出版时间2004-11
装帧平装
开本16开
纸张胶版纸
定价79元
货号29296352
上书时间2024-07-08
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【内容简介】:
Thisbookisintendedasatextbookforafirstcourseinthetheoryoffunctionsofonecomplexvariableforstudentswhoaremathematicallymatureenoughtounderstandandexecutearguments.Theactualpre-requisitesforreadingthisbookarequiteminimal;notmuchmorethanastiffcourseinbasiccalculusandafewfactsaboutpartialderivatives.Thetopicsfromadvancedcalculusthatareused（e.g.,Leibniz'srulefordiffer-entiatingundertheintegralsign）areprovedindetail.
【目录】:
Preface
Ⅰ.TheComplexNumberSystem
1.Therealnumbers
2.Thefieldofcomplexnumbers
3.Thecomplexplane
4.Polarrepresentationandrootsofcomplexnumbers
5.Linesandhalfplanesinthecomplexplane
6.Theextendedplaneanditssphericalrepresentation
Ⅱ.MetricSpacesandtheTopologyofC
1.Definitionandexamplesofmetricspaces
2.Connectedness
3.Sequencesandcompleteness
4.Compactness
5.Continuity
6.Uniformconvergence
Ⅲ.ElementaryPropertiesandExamplesofAnalyticFunctions
1.Powerseries
2.Analyticfunctions
3.Analyticfunctionsasmappings，M6biustransformations
Ⅳ.ComplexIntegration
1.Riemann-Stieltjesintegrals
2.Powerseriesrepresentationofanalyticfunctions
3.Zerosofananalyticfunction
4.Theindexofaclosedcurve
5.Cauchy'sTheoremandIntegralFormula
6.ThehomotopicversionofCauchy'sTheroremandsimpleconnectivity
7.Countingzeros;theOpenMappingTheorem
8.Goursat'sTheorem
Ⅴ.Singularities
1.Classificationofsingularities
2.Residues
3.TheArgumentPrinciple
VI The Maximum Modulus Theorem
ⅥI.CompactnessandConvergenceinthe
ⅦI.Runge'sTheorem
IX.AnalyticContinuationandRiemannSurfaces
X.HarmonicFunctions
ⅩI.EntireFunctions
ⅪI.TheRangeofanAnalyticFunction
AppendixA:CalculusforComplexComplexValuedFunctionsofandInterval
AppendixB:SuggestionsforFurtherStudyandBibliographicalNotes
References
Index
ListofSymbols
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